Parallel magnetic resonance imaging

ABSTRACT

The invention relates to a device ( 1 ) for magnetic resonance imaging of a body ( 7 ) placed in a stationary and substantially homogeneous main magnetic field. In order to provide an MR device ( 1 ) which is arranged to automatically select an optimum subsampling scheme for three-dimensional SENSE, the invention proposes to select the subsampling scheme such that the maximum number of folded-over image values is minimized and simultaneously distances between the positions of the folded-over image values within the predetermined field of view are maximized.

The invention relates to a device for magnetic resonance imaging of abody placed in a stationary and substantially homogeneous main magneticfield.

Furthermore, the invention relates to a method for magnetic resonanceimaging and to a computer program for a magnetic resonance imagingdevice.

In magnetic resonance imaging (MRI), pulse sequences consisting of RFand magnetic field gradient pulses are applied to an object (a patient)to generate phase encoded magnetic resonance signals, which are scannedby means of receiving antennas in order to obtain information from theobject and to reconstruct images thereof. Since its initial development,the number of clinical relevant fields of application of MRI has grownenormously. MRI can be applied to almost every part of the body, and itcan be used to obtain information about a number of important functionsof the human body. The pulse sequence which is applied during an MRIscan determines completely the characteristics of the reconstructedimages, such as location and orientation in the object, dimensions,resolution, signal-to-noise ratio, contrast, sensitivity for movements,etcetera. An operator of an MRI device has to choose the appropriatesequence and has to adjust and optimize its parameters for therespective application.

In known parallel MRI techniques, multiple receiving antennas withdifferent spatial sensitivity profiles are employed to reduce the scantime for a diagnostic image. This is achieved by acquiring a smaller setof phase encoded magnetic resonance signals than would actually benecessary to completely cover the predetermined field of view inaccordance with Nyquist's theorem.

In the known so-called SENSE technique (see for example Pruessmann etal, Magnetic Resonance in Medicine, volume 42, page 952, 1999), magneticresonance signals are acquired in a subsampled fashion while usingmultiple surface receiving coils of a magnetic resonance device. Thephase encoding steps in the k-space are increased relative to the phaseencoding steps actually required for the complete predetermined field ofview in geometrical space. This subsampling results in a reduced fieldof view. In conformity with the SENSE technique, images arereconstructed from the subsampled data separately for each receivingcoil. Because of the subsampling, these intermediary images containfold-over or so-called aliasing phenomena. On the basis of the knownspatial sensitivity profiles of the receiving coils, the individualcontributions to the folded-over image values of the intermediate imagescan be decomposed (unfolded) by means of matrix computations into imagevalues at spatial positions within the full field of view. In this way,the spatial encoding of the acquired magnetic resonance signals by thespatial sensitivity profiles of the receiving coils is made use of inorder to considerably accelerate the image acquisition procedure. Whenthe known SENSE technique is employed for the computation of the finalimage of the complete field of view, the ratio of the dimensions of thefull field of view relative to the reduced field is also referred to asreduction factor or simply as SENSE factor.

The above-described known SENSE technique can also be applied for threedimensional imaging (so-called 3D SENSE). In this case, subsampling isapplied in two phase encoding directions, for example the y- and thez-directions of the cartesian coordinate system of the MRI apparatus.Consequently, there are two independent reduction factors, usuallyreferred to as R_(y) and R_(x). It is a known problem in both 2D and 3DSENSE that the distances between positions within the field of view thathave to be unfolded during the SENSE reconstruction become small at highSENSE factors. Due to the correspondingly small differences between thelocal sensitivities of the receiving antennas, this results inundesirable image artifacts because of unstable matrix inversions. In 3DSENSE the distances between the folded-over positions are generallylarger than in the 2D case. Nonetheless, the problem occurs thatdepending on the selection of the independent reduction factors R_(y)and R_(z), the number of folded-over image values (so-called local SENSEfactor) varies a lot over the predetermined field of view. As a result,the image quality is not constant over the complete image. In someregions of the reconstructed image, the matrix inversion computations ofthe SENSE algorithm may even be underdetermined which has a very adverseeffect on local image quality.

Therefore it is readily appreciated that there is a need for an improveddevice for magnetic resonance imaging which enables the acquisition andreconstruction of high quality three-dimensional MR images using theSENSE technique. It is consequently the primary object of the presentinvention to provide an MR device which is arranged to automaticallyselect the subsampling scheme such that high local SENSE factors areavoided.

In accordance with the present invention, a device for magneticresonance imaging of a body placed in a stationary and substantiallyhomogeneous main magnetic field is disclosed. The device is providedwith receiving antennas which have different sensitivity profiles forreceiving phase encoded magnetic resonance signals from the body. Thedevice of the invention is arranged to acquire the magnetic resonancesignals with subsampling in two phase encoding directions incorrespondence with a predetermined field of view, reconstruct athree-dimensional image containing folded-over image values, andcalculate image values at spatial positions within said field of viewfrom the folded-over image values and from the sensitivity profiles ofthe receiving antennas. Therein the scheme of subsampling is selectedsuch that the maximum number of folded-over image values is minimizedand simultaneously the distances between the positions of thefolded-over image values are maximized.

The invention advantageously enables the generation of high quality MRimages using 3D sense, wherein the subsampling scheme in the two phaseencoding directions is selected automatically, for example on the basisof an overall SENSE factor as prescribed by a user of the MR device. Theinvention is based upon the insight that the quality of the finallyobtained image is optimum when the maximum number of the folded-overimage values (local SENSE factor) is minimized and simultaneously thedistance between the folded-over image positions (so-called foldingdistance) is maximized. Since the mutual dependencies between thereduction factors, the resulting local SENSE factors and the distancesbetween the folded-over image positions are theoretically known as such,it is easily possible to enable the automatic selection of thesubsampling scheme in accordance with the present invention by means ofan appropriate programming of the computer means of the magneticresonance imaging device.

In accordance with the present invention it is advantageous to selectthe scheme of subsampling in the two phase encoding directions such thatit corresponds to a triangular grid in k-space. In 3D SENSE the samplingof k-space in the phase encoding directions on a non-rectangular gridmakes it possible to achieve arbitrary and even non-integer reductionfactors. Furthermore, the triangular grid is ideal for use in accordancewith the present invention, since it inherently keeps the distancesbetween the folded-over image positions as large as possible andsimultaneously keeps the maximum number of folded-over image values aslow as possible. Thereby a more stable matrix inversion during SENSEreconstruction is achieved.

The proposed magnetic resonance imaging technique offers differentopportunities to select optimum values for the phase encoding stepsΔk_(y) and Δk_(z) in the two phase encoding directions (y- andz-directions). In general, these phase encoding steps obey to thefollowing:

${{\Delta \; k_{y}} = {{\frac{R_{y}}{{FOV}_{y}}\mspace{14mu} {and}\mspace{14mu} \Delta \; k_{z}} = \frac{R_{z}}{{FOV}_{z}}}},$

wherein FOV_(y) and FOV_(x) represent the dimensions of thepredetermined field of view in the two phase encoding directionsrespectively, and wherein R_(y) and R_(z) represent the correspondingreduction factors. For triangular sampling of k-space, the overall SENSEfactor in 3D SENSE can be defined as

$S = {\frac{1}{2}R_{y}{R_{z}.}}$

In order to optimize the image quality for a given SENSE factor inaccordance with the present invention, the reduction factors can beselected in accordance with the following relation:

${\frac{1}{\sqrt{3}}\frac{{FOV}_{y}}{R_{y}}} \leq \frac{{FOV}_{z}}{R_{z}} \leq {\sqrt{3}\frac{{FOV}_{y}}{R_{y}}}$

In the two extreme cases of this relation, the folded-over imagepositions are hexagonally distributed in geometrical space. Thus, thedistances between these positions are constant in all directions.

For given reduction factors R_(y) and R_(z), the maximum number offolded-over image positions (maximum local SENSE factor), again in thecase of triangular sampling of k-space, can be calculated by means ofthe following equation:

${S_{\max} = {{ceil}\left( {\frac{1}{2} \cdot {{ceil}\left( R_{y} \right)} \cdot {{ceil}\left( R_{z} \right)}} \right)}},$

wherein the ceil-function yields the lowest integer greater than orequal to its argument. It is practical to select the reduction factorsR_(y) and R_(z) in accordance with the invention, such that the aboverelation is fulfilled and simultaneously S_(max) acquires a minimumvalue.

In most practical cases, the field of view in one phase encodingdirection is at least a factor of two larger than in the other phaseencoding direction (FOV_(y)=2FOV_(z)). If a triangular sampling schemeis applied in such cases, it turns out to be particularly advantageousto select the reduction factors R_(y) and R_(z) for a predeterminedoverall SENSE factor S′, in accordance with

R_(z) = 2, R_(y) = 1  …  7  for  1 ≤ S ≤ 7, R_(z) = 3, R_(y) = 4.67  …  6  for  7 ≤ S ≤ 9, andR_(z) = 4, R_(y) = 4.5  …  8  for  9 ≤ S ≤ 16.

By increasing R_(y) while R_(z) is an integer a slow increase of themaximum number of folded-over image values is achieved. Thereby, highlocal SENSE factors are effectively prevented. When R_(z) increases by astep of one, the folding distance also increases. This helps to furtherimprove image quality. Since R_(z) can only acquire three differentinteger values in accordance with the above equations, there areadvantageously only two discontinuities when the overall SENSE factor iscontinuously increased, so that the image quality of the reconstructedimages behaves smoothly to the user of the magnetic resonance device ofthe invention. This advantageously allows the user a selectivefine-tuning of the overall SENSE factor.

The invention not only relates to a device but also to a method formagnetic resonance imaging of at least a portion of a body placed in astationary and substantially homogeneous main magnetic field, the methodcomprising the following steps:

acquiring magnetic resonance signals with subsampling in two phaseencoding directions in correspondence with a predetermined field ofview,

reconstructing a three-dimensional image containing folded-over imagevalues, and

calculating image values at spatial positions within said field of viewfrom the folded-over image values and sensitivity profiles of receivingantennas,

wherein the scheme of subsampling corresponds to a triangular grid andis selected such that the maximum number of folded-over image values isminimized and simultaneously the distances between the positions of thefolded-over image values within the field of view are maximized.

A computer program adapted for carrying out the imaging procedure of theinvention can advantageously be implemented on any common computerhardware, which is presently in clinical use for the control of magneticresonance scanners. The computer program can be provided on suitabledata carriers, such as CD-ROM or diskette. Alternatively, it can also bedownloaded by a user from an internet server.

The following drawings disclose preferred embodiments of the presentinvention. It should be understood, however, that the drawings aredesigned for the purpose of illustration only and not as a definition ofthe limits of the invention. In the drawings

FIG. 1 shows an embodiment of a magnetic resonance scanner according tothe invention,

FIG. 2 shows a triangular sampling scheme in accordance with theinvention,

FIG. 3 shows a diagrammatic representation of the selection of thesubsampling scheme in accordance with the invention.

In FIG. 1 a magnetic resonance imaging device 1 in accordance with thepresent invention is shown as a block diagram. The apparatus 1 comprisesa set of main magnetic coils 2 for generating a stationary andhomogeneous main magnetic field and three sets of gradient coils 3, 4and 5 for superimposing additional magnetic fields with controllablestrength and having a gradient in a selected direction. Conventionally,the direction of the main magnetic field is labelled the z-direction,the two directions perpendicular thereto the x- and y-directions. Thegradient coils are energized via a power supply 11. The apparatus 1further comprises a radiation emitter 6, an antenna or coil, foremitting radio frequency (RF) pulses to a body 7, the radiation emitter6 being coupled to a modulator 8 for generating and modulating the RFpulses. Also provided are receiving antennas 10 a, 10 b, 10 c forreceiving the MR signals, the receiving antennas can for example beseparate surface coils with different spatial sensitivity profiles. Thereceived MR signals are input to a demodulator 9. The modulator 8, theemitter 6 and the power supply 11 for the gradient coils 3, 4 and 5 arecontrolled by a control system 12 to generate the actual imagingsequence for SENSE imaging in accordance with the above-describedinvention. The control system is usually a microcomputer with a memoryand a program control. For the practical implementation of the inventionit comprises a programming with a description of an imaging procedure asdescribed above. The demodulator 9 is coupled to a data processing unit14, for example a computer, for transformation of the received magneticresonance signals into an image in accordance with the known SENSEunfolding algorithm. This image can be made visible, for example, on avisual display unit 15.

FIG. 2 illustrates a triangular sampling grid in k-space as it canadvantageously be employed in accordance with the invention. The vectorsΔk_(y), Δk_(z) and Δk_(h) define the depicted triangular grid. Δk_(h)points to the center of the square defined by Δk_(y) and Δk_(z). For agiven field of view defined by the dimensions FOV_(y) and FOV_(z) ingeometrical space, the following equation applies:

${{\Delta \; k_{y}} = {{\frac{R_{y}}{{FOV}_{y}}\mspace{14mu} {and}\mspace{14mu} \Delta \; k_{z}} = \frac{R_{z}}{{FOV}_{z}}}},$

wherein R_(y) and R_(z) represent the reduction factors of subsamplingin the respective directions.

The diagram of FIG. 3 visualizes the automatic selection of the optimumtriangular subsampling scheme in accordance with the invention. Thecurve 20 shows the mutual dependency of R_(y) and R_(z) for a givenoverall SENSE factor obeying to the equation

$S = {\frac{1}{2}R_{y}{R_{z}.}}$

S might for example be prescribed by the user of an MR device featuringthe invention. In the area of the diagram as defined by the two dashedlines 21, the relation

${\frac{1}{\sqrt{3}}\frac{{FOV}_{y}}{R_{y}}} \leq \frac{{FOV}_{z}}{R_{z}} \leq {\sqrt{3}\frac{{FOV}_{y}}{R_{y}}}$

is fulfilled. In this region the distances between folded-over imageposition are maximum. The combination of the reduction factors R_(y) andR_(z) lying on the section 22 of the curve 20 is to be selected suchthat the folding distance is optimized in terms of image quality. Thegrid 23 depicted in FIG. 3 illustrates areas with different maximumnumbers S_(max) of folded-over image positions. In the embodied case oftriangular sampling of k-space, the maximum local SENSE factor S_(max)can be calculated in the different areas according to the equation

$S_{\max} = {{{ceil}\left( {\frac{1}{2} \cdot \; {{ceil}\left( R_{y} \right)} \cdot {{ceil}\left( R_{z} \right)}} \right)}.}$

For optimum image quality the reduction factors R_(y) and R_(z) lying onthe section 22 are automatically selected for which S_(max) acquires aminimum value.

1. Device for magnetic resonance imaging of a body placed in astationary and substantially homogeneous main magnetic field, withreceiving antennas for receiving phase encoded magnetic resonancesignals from the body, which receiving antennas have sensitivityprofiles, wherein the device is arranged to acquire the magneticresonance signals with subsampling in two phase encoding directions incorrespondence with a predetermined field of view, reconstruct athree-dimensional image containing folded-over image values, andcalculate image values at spatial positions within said field of viewfrom the folded-over image values and the sensitivity profiles of thereceiving antennas, wherein the scheme of subsampling is selected suchthat the maximum number of folded-over image values is minimized andsimultaneously the distances between the positions of the folded-overimage values are maximized.
 2. Device of claim 1, wherein the scheme ofsubsampling in the two phase encoding directions corresponds to atriangular grid.
 3. Device of claim 2, wherein phase encoding stepsΔk_(y) and Δk_(z) in the two phase encoding directions are employed inaccordance with${{\Delta \; k_{y}} = {{\frac{R_{y}}{{FOV}_{y}}\mspace{14mu} {and}\mspace{14mu} \Delta \; k_{z}} = \frac{R_{z}}{{FOV}_{z}}}},$wherein FOV_(y) and FOV_(z) represent the predetermined field of view inthe two phase encoding directions respectively, and wherein R_(y) andR_(z) represent reduction factors being larger than one.
 4. Device ofclaim 3, wherein the reduction factors are selected in accordance withthe relation${\frac{1}{\sqrt{3}}\frac{{FOV}_{y}}{R_{y}}} \leq \frac{{FOV}_{z}}{R_{z}} \leq {\sqrt{3}{\frac{{FOV}_{y}}{R_{y}}.}}$5. Device of claim 3, wherein for a predetermined SENSE factorS=½R_(y)R_(z), the reduction factors R_(y) and R_(z) are selected inaccordance withR_(z) = 2, R_(y) = 1  …  7  for  1 ≤ S ≤ 7, R_(z) = 3, R_(y) = 4.67  …  6  for  7 ≤ S ≤ 9, andR_(z) = 4, R_(y) = 4.5  …  8  for  9 ≤ S ≤
 16. 6. Method formagnetic resonance imaging of at least a portion of a body placed in astationary and substantially homogeneous main magnetic field, the methodcomprising the following steps: acquiring magnetic resonance signalswith subsampling in two phase encoding directions in correspondence witha predetermined field of view, reconstructing a three-dimensional imagecontaining folded-over image values, and calculating image values atspatial positions within said field of view from the folded-over imagevalues and sensitivity profiles of receiving antennas, wherein thescheme of subsampling corresponds to a triangular grid and is selectedsuch that the maximum number of folded-over image values is minimizedand simultaneously the distances between the positions of thefolded-over image values are maximized.
 7. Method of claim 6, whereinphase encoding steps Δk_(y) and Δk_(z) in the two phase encodingdirections are prescribed in accordance with${{\Delta \; k_{y}} = {{\frac{R_{y}}{{FOV}_{y}}\mspace{14mu} {and}\mspace{14mu} \Delta \; k_{z}} = \frac{R_{z}}{{FOV}_{z}}}},$wherein FOV_(y) and FOV_(x) represent the predetermined field of view inthe two phase encoding directions respectively, and wherein R_(y) andR_(z) represent reduction factors being larger than one, and wherein thereduction factors are selected in accordance with the relation${\frac{1}{\sqrt{3}}\frac{{FOV}_{y}}{R_{y}}} \leq \frac{{FOV}_{z}}{R_{z}} \leq {\sqrt{3}{\frac{{FOV}_{y}}{R_{y}}.}}$8. Method of claim 7, wherein for a predetermined SENSE factor${S = {\frac{1}{2}R_{y}R_{z}}},$ the reduction factors R_(y) and R_(z)are selected in accordance withR_(z) = 2, R_(y) = 1  …  7  for  1 ≤ S ≤ 7, R_(z) = 3, R_(y) = 4.67  …  6  for  7 ≤ S ≤ 9, andR_(z) = 4, R_(y) = 4.5  …  8  for  9 ≤ S ≤
 16. 9. Computerprogram for a magnetic resonance imaging device, with instructions foracquiring magnetic resonance signals with subsampling in two phaseencoding directions in correspondence with a user predetermined field ofview, reconstructing a three-dimensional image containing folded-overimage values, and calculating image values at spatial positions withinsaid field of view from the folded-over image values and sensitivityprofiles of receiving antennas, wherein the scheme of subsamplingcorresponds to a triangular grid and is selected such that the maximumnumber of folded-over image values is minimized and simultaneously thedistances between the positions of the folded-over image values aremaximized.
 10. Computer program of claim 9, wherein phase encoding stepsΔk_(y) and Δk_(z) in the two phase encoding directions are employed inaccordance with${{\Delta \; k_{y}} = {{\frac{R_{y}}{{FOV}_{y}}\mspace{14mu} {and}\mspace{14mu} \Delta \; k_{z}} = \frac{R_{z}}{{FOV}_{z}}}},$wherein FOV_(y) and FOV_(x) represent the predetermined field of view inthe two phase encoding directions respectively, and wherein R_(y) andR_(z) represent reduction factors being larger than one, and wherein thereduction factors are selected in accordance with the relation${\frac{1}{\sqrt{3}}\frac{{FOV}_{y}}{R_{y}}} \leq \frac{{FOV}_{z}}{R_{z}} \leq {\sqrt{3}{\frac{{FOV}_{y}}{R_{y}}.}}$larger than one, and wherein the reduction factors are selected inaccordance with the relation${\frac{1}{\sqrt{3}}\frac{{FOV}_{y}}{R_{y}}} \leq \frac{{FOV}_{z}}{R_{z}} \leq {\sqrt{3}{\frac{{FOV}_{y}}{R_{y}}.}}$